Lesson 3: Scientific Notation

Why do scientists use scientific notation?

How do you convert standard numbers into scientific notation and vice versa?

How do significant figures relate to precision in measurements?

What is the difference between accuracy and precision, and why does it matter in science?

How can scientific notation help compare very large or very small values in data?

Scientific notation

Exponent

Base 10

Standard form

Accuracy

Precision

Significant figures

Measurement error

• HS-PS1-3 – Use scientific notation to represent and interpret very large or very small quantities in measurements.
• HS-PS3-1 / HS-ESS2-5 – Apply accuracy and precision concepts when collecting and analyzing scientific data.

Students will practice interpreting data expressed in scientific notation, a common requirement on standardized assessments.

Students will analyze and calculate measurements, connecting mathematical representations to scientific phenomena.

Students will improve quantitative reasoning and problem-solving skills by comparing large or small numbers in meaningful contexts.

NGSS Crosscutting Concepts

Scale, Proportion, and Quantity

Patterns

Cause and Effect

Systems and System Models

Students will learn to convert very large and very small numbers into scientific notation and interpret them in scientific contexts. They will practice using significant figures to reflect the precision of measurements and analyze data for both accuracy and precision.

The lesson emphasizes the importance of reliable measurements and the ability to communicate very large or very small quantities clearly. Students will apply these skills to hands-on examples, including calculations from lab experiments or real-world datasets.

Scientific notation is used in astronomy, chemistry, physics, and technology to handle extremely large distances, very small particles, or enormous quantities (e.g., population, energy, or data storage). Students will see how these skills allow scientists and engineers to communicate and analyze information effectively.

Students may confuse the exponent in scientific notation with a regular multiplication factor.

Students may forget to adjust significant figures correctly when converting numbers.

Students may think large numbers don’t need scientific notation.

Students may misunderstand the difference between accuracy and precision.

Scaffolded practice problems with step-by-step guidance

Tiered assignments for different skill levels

Use of calculators and conversion charts

Peer collaboration to check conversions and significant figures

Hands-on activities applying scientific notation to real-world data (e.g., distances in space, mass of molecules)

• Checkpoints during practice problems and conversions

• Quizzes on scientific notation, significant figures, and measurement accuracy/precision

• Lab exercises using scientific notation to record and analyze data

• Unit Test

• Participation in class discussions and peer review of calculations

• Slides and handouts on scientific notation and significant figures

• Calculators

• Lab worksheets with measurement data

• Practice problems and conversion tables

• Real-world datasets for student analysis (astronomy, chemistry, or physics examples)